Understanding the Missing Stages in Simplifying Expressions

[exequor]

can someone explain to me the stages that are missing in the expression in the attached picture. i think that it has to do with identities but in the book that i got it from did not explain clearly how they went from one line to another. i will appreciate the help very much.

 

[gnome]

It uses this identity:

$$sin(x)cos(y) = \frac{1}{2}\left(sin(x+y) + sin(x-y)\right)$$

$$x = \theta$$
$$y = \theta - 30^o$$

 

[exequor]

thanx very much gnome i thought that i would never get a response